Question

direct sum of injective hull of two modules is equal to the injective hull of direct sum of those modules

score 577 · Answer 1 · 2026-05-02 23:48:47

577

Views

direct sum of injective hull of two modules is equal to the injective hull of direct sum of those modules

Published on 02 May 2026 - 23:48

score 155 · Answer 2 · 2026-05-07 06:51:04

155

Views

injective hull of a ring that is not integral domain

Published on 07 May 2026 - 6:51

score 308 · Answer 3 · 2026-04-29 12:43:00

308

Views

Decomposition of injective modules over polynomial rings

Published on 29 Apr 2026 - 12:43

score 190 · Answer 4 · 2026-05-05 02:07:27

190

Views

Problem based on Projective and Injective Module

Published on 05 May 2026 - 2:07

score 428 · Answer 5 · 2026-05-03 02:19:39

428

Views

Example of reduced module

Published on 03 May 2026 - 2:19

score 114 · Answer 6 · 2026-04-29 12:42:56

114

Views

Injective object in the category of projective systems of $R$-modules.

Published on 29 Apr 2026 - 12:42

score 97 · Answer 7 · 2026-05-05 16:25:33

97

Views

Injective Linear Transformation $K[x]_{\leq 4}\rightarrow V$

Published on 05 May 2026 - 16:25

score 431 · Answer 8 · 2026-05-10 13:34:40

431

Views

For $d\mid m$, $\mathbb{Z}/d\mathbb{Z}$ is not an injective $\mathbb{Z}/m\mathbb{Z}$-module when some prime divides $d$ and $\frac{m}{d}$

Published on 10 May 2026 - 13:34

score 362 · Answer 9 · 2026-05-03 01:07:54

362

Views

$\mathbb{Q}_{\mathbb{Z}}$ is an injective hull of $\mathbb{Z}$

Published on 03 May 2026 - 1:07

score 352 · Answer 10 · 2026-04-29 15:04:32

352

Views

Element in a finitely generated torsion module on a PID with smallest non-zero annihilator

Published on 29 Apr 2026 - 15:04

score 1.1k · Answer 11 · 2026-05-05 18:28:58

1.1k

Views

Let $R$ be a Noetherian Ring, then the category of $R$-modules has enough injectives

Published on 05 May 2026 - 18:28

score 773 · Answer 12 · 2026-05-02 12:39:43

773

Views

If $Q$ is injective, then $\text{Hom}_{\mathbb Z}(R, Q)$ is injective.

Published on 02 May 2026 - 12:39

score 1.6k · Answer 13 · 2026-05-10 12:32:29

1.6k

Views

Prove that no $\mathbb{Z}$-module is both projective and injective

Published on 10 May 2026 - 12:32

score 1k · Answer 14 · 2026-05-10 12:33:21

1k

Views

Quotient of injective module which is not injective

Published on 10 May 2026 - 12:33

score 344 · Answer 15 · 2026-05-02 09:59:24

344

Views

Injective module

Published on 02 May 2026 - 9:59

List Question

direct sum of injective hull of two modules is equal to the injective hull of direct sum of those modules

injective hull of a ring that is not integral domain

Decomposition of injective modules over polynomial rings

Problem based on Projective and Injective Module

Example of reduced module

Injective object in the category of projective systems of $R$-modules.

Injective Linear Transformation $K[x]_{\leq 4}\rightarrow V$

For $d\mid m$, $\mathbb{Z}/d\mathbb{Z}$ is not an injective $\mathbb{Z}/m\mathbb{Z}$-module when some prime divides $d$ and $\frac{m}{d}$

$\mathbb{Q}_{\mathbb{Z}}$ is an injective hull of $\mathbb{Z}$

Element in a finitely generated torsion module on a PID with smallest non-zero annihilator

Let $R$ be a Noetherian Ring, then the category of $R$-modules has enough injectives

If $Q$ is injective, then $\text{Hom}_{\mathbb Z}(R, Q)$ is injective.

Prove that no $\mathbb{Z}$-module is both projective and injective

Quotient of injective module which is not injective

Injective module

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